Related papers: The Riemann tensor for nonholonomic manifolds

Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann…

One (actually, almost the only effective) way to prove formality of a differentiable manifold is to be able to produce a suitable derivation $\delta$ such that $d\delta$-lemma holds. We first show that such derivation $\delta$ generates a…

In this paper, we study and partially classify those Riemannian man-ifolds carrying a non-identically vanishing function f whose Hessian is minus f times the Ricci-tensor of the manifold.

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

The Tolman~VII solution, an exact analytic solution to the spherically symmetric, static Einstein equations with a perfect fluid source, has many characteristics that make it interesting for modelling high density physical astronomical…

We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal approaches within a unifying framework. First, we establish a…

In this paper, we show several vanishing type theorems for $p$-harmonic $\ell$-forms on Riemannian manifolds ($p\geq2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of ${N}^{n+m}$ with flat normal bundle, we…

The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part $F$ of basic…

The Lagrangian formalism for tensor fields over differentiable manifolds with contravariant and covariant affine connections (whose components differ not only by sign) and metrics [$(\bar{L}_n,g)$-spaces] is considered. The functional…

For a complete Riemannian manifold $M$ with an (1,1)-elliptic Codazzi self-adjoint tensor field $A$ on it, we use the divergence type operator ${L_A}(u): = div(A\nabla u)$ and an extension of the Ricci tensor to extend some major comparison…

In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions…

Sectional curvature bounds are of central importance in the study of Riemannian manifolds, both in smooth differential geometry and in the generalized synthetic setting of Alexandrov spaces. Riemannian metrics along with metric spaces of…

We introduce and study the notion of null manifold. This is a smooth manifold ${\mathcal N}$ endowed with a degenerate metric $\gamma$ with one-dimensional radical at every point. We also define the notion of ruled null manifold, which is a…

Almost Finsler manifolds and partial Finsler manifolds are introduced, extending the standard definition of a Finsler manifold to allow for a nontrivial slit containing points fixed under homogeneous scaling and for metrics where the…

In 1992, Agache and Chaple introduced the concept of a semi-symmetric non-metric connection([1]). The semi-symmetric non-metric connection does not satisfy the Schur`s theorem. The purpose of the present paper is to study some properties of…

We explicitly compute the spectral metric, torsion and Einstein tensors for a nontrivial spectral triple on a noncommutative torus, with the Dirac operator related to the fully equivariant Dirac by a partial conformal rescaling (as…

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a…

We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the…

This paper is about geometric and Riemannian properties of Engel structures, i.e. maximally non-integrable $2$-plane fields on $4$-manifolds. Two $1$-forms $\alpha$ and $\beta$ are called Engel defining forms if…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…